Static particles freak out after certain amount of time?
Additionally (re-editing my last answer)
I am attaching a blend file in which I noticed that I had to use Brownian Force and Damp instead of Turbulence or any other kind of field.



This should do the work.

Blender File

In order to keep the particles still you must turn off the Normal property in the Emiter Geometry under the tab Velocity of your Particles System.



The second thing that you have to do, so your particles will not go towards the "ground plane" is to turn off the Gravity affection in the "Field Weights" Tab.
From this panel you will also set the desired affection from other fields (such as Turbulence, Wind, Vortex etc) that you may use to give to your particles the kind of movement you are looking for.